Ari has wealth of $300,000, and is a firm believer in expected utility theory. Suppose the...

  

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Ari has wealth of $300,000, and is a firm believer in expected utility theory. Suppose the table below reflects the marginal utility he derives from each of the listed dollars of his wealth. Dollar # 299,991 299,992 299,993 299,994 299,995th 299,996th 299,997 299,998th 299,999th 300,000th 300,001st 300,002nd 300,003rd 300,004th 300,005th 300,006th 300,007th 300,008th 300,009th 300,010th 300,011th 300,012 300,013th 300,014th 300,015th 300,016th 300,017th 300,018th 300,019 300,020 Marginal Utility 310 300 291.3 282.8 274.5 266.4 258.4 250.5 242.7 235 227.4 219.9 212.5 205.2 198.2 191.7 185.5 179.4 173.4 167.9 162.5 157.2 152 146.9 142.1 137.5 133.3 129.3 125.4 121.6 a. Would Ari accept the following offer from his broker? "There is an investment opportunity available! The cost is $10. If you take it, there is a 50% chance you will lose your entire investment (the full $10). But there is also a 50% chance that the investment will work out, and you will get back $25 (earning a $15 return on net)." b. What if the offer was as above, except that it paid $24 in the event that the investment worked out instead? Would Ari accept it now? [Note: without submitting anything, consider whether your answers in (a) and (b) seem reasonable. As in, would you be surprised if someone had the preferences you found for Ari in (a) and (b), independent of any formal computations of utility?] c. Suppose you want to convince Ari that expected utility theory would have a hard time explaining his preferences. To do this, you walk him through an exercise taking expected utility theory as given, to demonstrate how assuming expected utility theory is an accurate description of behavior leads to weird results (hint: this is similar to what is done in the Rabin and Thaler reading). To start, you ask Ari whether his response to the question in (b) would be different if his starting wealth was $300,020. He confirms that his answer would be the same. Given this preference and using the table above, compute the maximum possible utility that Ari would get from the 14 marginal dollars from the 300,021" to the 300,034th (as in, what is the maximum total utility he could get from those 14 dollars together?). d. Using your answer in (c) and keeping diminishing marginal utility in mind, what does this mean about the maximum possible marginal utility that Ari could be getting from the 300,034 dollar alone? e. Compute and consider the ratio between the marginal utility Ari gets from his 299,991" dollar, given in the table) and the maximum possible marginal utility he could get from his 300,034 dollar, as you computed in (d). Using this ratio, make an argument in no more than 3 sentences that Ari's preferences here cast doubt on how accurate expected utility theory. in explaining Ari's risk attitudes and decisions. Ari has wealth of $300,000, and is a firm believer in expected utility theory. Suppose the table below reflects the marginal utility he derives from each of the listed dollars of his wealth. Dollar # 299,991 299,992 299,993 299,994 299,995th 299,996th 299,997 299,998th 299,999th 300,000th 300,001st 300,002nd 300,003rd 300,004th 300,005th 300,006th 300,007th 300,008th 300,009th 300,010th 300,011th 300,012 300,013th 300,014th 300,015th 300,016th 300,017th 300,018th 300,019 300,020 Marginal Utility 310 300 291.3 282.8 274.5 266.4 258.4 250.5 242.7 235 227.4 219.9 212.5 205.2 198.2 191.7 185.5 179.4 173.4 167.9 162.5 157.2 152 146.9 142.1 137.5 133.3 129.3 125.4 121.6 a. Would Ari accept the following offer from his broker? "There is an investment opportunity available! The cost is $10. If you take it, there is a 50% chance you will lose your entire investment (the full $10). But there is also a 50% chance that the investment will work out, and you will get back $25 (earning a $15 return on net)." b. What if the offer was as above, except that it paid $24 in the event that the investment worked out instead? Would Ari accept it now? [Note: without submitting anything, consider whether your answers in (a) and (b) seem reasonable. As in, would you be surprised if someone had the preferences you found for Ari in (a) and (b), independent of any formal computations of utility?] c. Suppose you want to convince Ari that expected utility theory would have a hard time explaining his preferences. To do this, you walk him through an exercise taking expected utility theory as given, to demonstrate how assuming expected utility theory is an accurate description of behavior leads to weird results (hint: this is similar to what is done in the Rabin and Thaler reading). To start, you ask Ari whether his response to the question in (b) would be different if his starting wealth was $300,020. He confirms that his answer would be the same. Given this preference and using the table above, compute the maximum possible utility that Ari would get from the 14 marginal dollars from the 300,021" to the 300,034th (as in, what is the maximum total utility he could get from those 14 dollars together?). d. Using your answer in (c) and keeping diminishing marginal utility in mind, what does this mean about the maximum possible marginal utility that Ari could be getting from the 300,034 dollar alone? e. Compute and consider the ratio between the marginal utility Ari gets from his 299,991" dollar, given in the table) and the maximum possible marginal utility he could get from his 300,034 dollar, as you computed in (d). Using this ratio, make an argument in no more than 3 sentences that Ari's preferences here cast doubt on how accurate expected utility theory. in explaining Ari's risk attitudes and decisions.

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answers Would Ari accept the following offer from his broker There is an investment opportunity available The cost is 10 If you take it there is a 50 chance you will lose your entire investment the fu... View the full answer